Elsevier

Fuzzy Sets and Systems

Volume 155, Issue 1, 1 October 2005, Pages 150-163
Fuzzy Sets and Systems

On central algorithms of approximation under fuzzy information

https://doi.org/10.1016/j.fss.2005.05.018Get rights and content

Abstract

We consider the problem of approximation of an operator by information described by n real characteristics in the case when this information is fuzzy. We develop the well-known idea of an optimal error method of approximation for this case. It is a method whose error is the infimum of the errors of all methods for a given problem characterized by fuzzy numbers in this case. We generalize the concept of central algorithms, which are always optimal error algorithms and in the crisp case are useful both in practice and in theory. In order to do this we define the centre of an L-fuzzy subset of a normed space. The introduced concepts allow us to describe optimal methods of approximation for linear problems using balanced fuzzy information.

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